Abstract

Measurements of ice deformation at the surface and at depth in the Athabasca Glacier, Canada, reveal for the first time the pattern of flow in a nearly complete cross section of a valley glacier, and make it possible to test the applicability of experimental and theoretical concepts in the analysis of glacier flow. Tilting in nine boreholes (depth about 300 m, eight holes essentially to the bottom) was measured with a newly developed electrical inclinometer, which allows a great increase in the speed and accuracy with which borehole configurations can be determined, in comparison with earlier methods. The measurements define the distribution of the velocity vector and the strain-rate tensor over 70% of the area of the glacier cross section.

The main longitudinal component of flow has the following general features: (1) basal sliding velocity which exceeds 70% of the surface velocity over half of the width of the glacier, (2) marginal sliding velocity (not more than a few meters per year) much less than basal sliding velocity at the centerline (about 40 m yr(-1)), (3) marginal shear strain rate near the valley walls two to three times larger than the basal shear strain rate near the centerline (0.1 yr(-1)).

The observed longitudinal flow is significantly different from that expected from theoretical analysis of flow in cylindrical channels (Nye, 1965). The relative strength of marginal and basal shear strain rate is opposite to that expected from theory. In addition, the longitudinal flow velocity averaged over the glacier cross section (which determines the flux of ice transported) is larger by 11% than the average flow velocity seen at the glacier surface, whereas it would be 2% smaller if the theoretical prediction were correct. These differences are caused to a large extent by the constant sliding velocity assumed in the theoretical analysis, which contrasts strongly with the actual distribution of sliding. The observed relation between marginal and basal sliding velocity is probably a general flow feature in valley glaciers, and may be caused by lateral variation of water pressure at the ice-rock contact. The observed pattern of longitudinal velocity over the section also shows in detail certain additional features incompatible with the theoretical treatment, even after the difference in boundary conditions (distribution of sliding velocity) is taken into account.

Longitudinal strain rate (a compression of about 0.02 yr(-1) at the surface) decreases with depth, becoming nearly 0 at the bed in the center of the glacier. The depth variation cannot be explained completely by overall bending of the ice mass as a result of a longitudinal gradient in the curvature of the bed, and is at variance with existing theories, which require the longitudinal strain rate to be constant with depth.

Motion transverse to the longitudinal flow occurs in a roughly symmetric pattern of diverging marginward flow, with most of the lateral transport occurring at depth in a fashion reminiscent of extrusion flow. The observed lateral velocities averaged over depth (up to 1.9 m yr(-1)) are compatible with the lateral flux required to maintain equilibrium of the marginal portions of the glacier surface under ablation (3.7 m yr(-1)) and are driven by the convex transverse profile of the ice surface.

When the measured strain-rate field is analyzed on the basis of the standard assumption that the shear stress parallel to the glacier surface varies linearly with depth, the rheological behavior in the lower one-half to two-thirds of the glacier is found compatible with a power-type flow law with n = 5.3. However, the upper one-third to one-half of the glacier constitutes an anomalous zone in which this treatment gives physically unreasonable rheological behavior. In a new method of analysis, rheological parameters are chosen so as to minimize the fictitious body forces that appear as residuals in the equilibirum equations when evaluated for the measured strain-rate field. This new method requires no a priori assumptions about the stress distribution, although for simplicity in application, the mean stress is assumed constant longitudinally. This treatment shows that the anomalies in the near-surface zone are due to significant departures from linear dependence of shear stress on depth, and gives a flow-law exponent of n = 3.6, which is closer than n = 5.3 to values determined by laboratory experiments on ice.